CBSE Class 10 Mathematics Important Questions for Exam 2023 (Chapter - Arithmetic Progression)

 

These Mathematics Questions of Chapter {Arithmetic Progression} are important for CBSE Examination 2023.

1)      Find the 9^th term from the end of the A.P is 5, 9, 13, ….., 185.

2)      The 4^th term of an A.P is zero. Prove that the 25^th term of the A.P is three times its 11^th term.

3)      How many terms of the A.P = 18, 16, 14, ……. Be taken so that their sum is zero.

4)      If sum of the first 7 terms of an A.P is 49 and that of its first 17 terms is 289, find the sum of first n terms of an A.P.

5)      How many terms of the A.P 65, 60, 55, …….. be taken so that their sum is zero.

6)      How many terms of the A.P. 27, 24, 21,….. should be taken so that their sum is zero.

7)      Find the natural numbers between 101 and 999 which are divisible by both 2 and 5.

8)      The sum of the first n terms of an A.P. is 3n² + 6n. Find the n^th term of this A.P.

9)      The first and the last terms of an A.P are 5 and 45 respectively. If the sum of all its terms is 400, find its common difference.

10)  The n^th term of an A.P. is a_n = 2n + 1, find its sum.

11)  Find the number of all three digit natural numbers which are divisible by 9.

12)  The 9^th term of an A.P. is equal to 6 times of its second term. If its 5^th term is 22, find the A.P.

13)  In an A.P., given a = -4 and d = 3, find its 20^th term and the sum of first 20^th terms.

14)  The 8^th term of an A.P. is equal to three times its third term. If its 6^th term is 22, find the A.P.

15)  Sum of the first 20^th terms of an A.P. is -240 and its first term is 7. Find its 24^th term.

16)  If for a given A.P. a = 7, a₁₃ = 35, then find S₁₃.

17)  The 16^th term of an A.P. is 1 more than twice its 8^th term. If the 12^th term of the A.P. is 47, then find its n^th term.

18)  Find the value of p, If the numbers x, 2x + p, 3x + 6 are three consecutive terms of an A.P.

19)  Find the common difference of an A.P. whose first term is ½ and the 8^th term is 17/6. Also write the 4^th term.

20)  The angles of a triangle are in A.P. The greatest angle is twice the least. Find all angles of the triangle.

21)  The sum of three numbers in A.P. is 12 and sum of their cubes is 288. Find the numbers.

22)  The digit of a positive number of three digits are in A.P. and their sum is 15. The number obtain by reversing the digits is 594 less than the original number. Find the number.

23)  The sums of first n terms of three A.P. are S₁, S₂, and S₃ respectively. The first term of each A.P. is 1 and their common differences are 1, 2 and 3 respectively. Prove that S₁ + S₃ = 2S₂.

24)  If the 7^th term of an A.P. is 1/9 and the 9^th term is 1/7, find its 63^rd term.

25)  The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28^th term of this A.P.

 

26)  The sum of the 5^th and the 9^th terms of an A.P. is 30. If its 25^th term is 3 times its 8^th term, find the A.P.

27)  The sum of first m terms of an A.P. is 4m² – m. If its n^th term is 107, find the value of n. Also find the 21^st term of an A.P.

28)  Find the sum of all multiples of 9 lying between 400 and 800.

29)  If the sum of the first 7 terms of an A.P. is 119 that of the first 17 terms is 714, find the sum of its first n terms.

30)  Find the sum of all multiples of 7 lying between 500 and 900.

31)  Find the sum of all three digits natural numbers, which are multiples of 11.

32)  Find the sum of the first 50 odd natural numbers.

33)  How many terms of the A.P. 9, 17, 25,… must be taken to get a sum of 450.

34)  Find the sum of all multiples of 9 lying between 300 and 700.

35)  A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows : Rs. 200 for the first day, Rs. 250 for the second day, Rs. 300 for the third day, etc., the penalty for each succeeding day being Rs. 50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days. 

36)  Which term of the A.P. 121, 117, 113, …… is its first negative term?

37)  The houses in a row are numbered consecutively from 1 to 49. Show that there exists a value of X such that sum of numbers of houses proceeding the house numbered X is equal to sum of the numbers of houses following X.

38)  A thief after committing a theft, runs at a uniform sped of 50 m/minute. After 2 minutes, a policeman runs catch him. He goes 60 m in first minute and increases his speed by 5 m/minute every succeeding minute. After how many minutes, their policeman will catch the thief?

39)  In an A.P. of 50 terms the sum of first 10 terms is 210 and the sum of its last 15 terms is 2565, Find the A.P.

40)  If S_n denotes the sum of first n terms of an A.P., Prove that S₃₀ = 3(S₂₀ – S₁₀).

41)  Find the common difference of an A.P. whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.

42)  The 17^th term of an A.P. is 5 more than twice its 8^th term. If the 11^th term of the A.P. is 43, then find its n^th term.

43)  A sum of Rs. 1600 is to be used to give ten cash prizes to students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize, find the value of each of the prizes.

44)  If the m^th term of an A.P. is 1/n and n^th term is 1/m, then show that the sum of mn term is ½(mn + 1).

45)  If the sum of first m term of an A.P. is n and the sum of first n term is m, then show that the sum of its                  first (m + n) term is – (m + n).

46)  Jaipal singh repays the total loan of 118000 by paying every month starting with the first installment of Rs. 1000. If he increases the installment by Rs. 100 every month, what amount will be paid by him in the 30^th installment? What amount of loan does he still have to pay after 30^th installment?

47)  A sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize, find the value of each of the prize.

48)  For what value of k will K + 9, 2k – 1 and 2k + 7 are the consecutive terms of an A.P.

49)  Find the 7^th term of the sequence whose n^th term is given by a_n = (-1)^n-1. n³.

50)  Is 6 a term of the A.P. 7, 10, 13, …..?

51)  If 21, a , b, -3 are in A.P. then find the value of (a + b).

52)  For an A.P. If a₁₈ – a₁₄ = 32, then find the common difference.

53)  How many two digit numbers are divisible by 3?

54) If the numbers x – 2, 4x – 1 and 5x + 2 are in A.P. Find the value of x.